NOT FOR PUBLICATION
Online Appendix to “Can Higher Prices Stimulate Product Use?
Evidence from a Field Experiment in Zambia”
November 3, 2009
A
Formal Model
In this section, we present a simple model of Clorin purchase and use, allowing for sunk-cost effects
using Eyster’s (2002) framework. At the end of the section, we discuss how our results would
generalize to alternative models of sunk-cost psychology.
A.1
Material Payoffs
We will consider household behavior in some number of periods indexed by t. In each period t,
each household i must decide whether to purchase Clorin and, if so, whether to use it in their
drinking water. In period t, each household i can decide to purchase Clorin for an exogenous,
possibly household-specific offer price pit ∈ (0, R] , where R > 0 is the retail price of Clorin. If the
household decides to buy Clorin, it may receive an exogenous discount, so that it will only have to
pay the transaction price p̃it ∈ [0, pit ]. We assume that households do not anticipate the possibility
of a discount, or, equivalently, that they consider the probability of a discount after purchase to be
negligible.
We experimentally manipulate the prices faced by households in a particular period t0 . For
simplicity, we will assume that in all previous and subsequent periods, Clorin retails at R, and
there are no discounts. That is, we assume that, in any period t 6= t0 , pit = p̃it = R. In period
t0 , however, prices pit0 and p̃it0 are randomly assigned across households in a manner specified in
section IIExperimental and Survey Designsection.2 of the paper. We will also assume for simplicity
that the utility from using Clorin in a given period is independent of its use in previous or future
periods.1
We will think of a period as approximately one month, about the time it takes to use up a
bottle of Clorin in drinking water for a family of six. We assume that Clorin cannot be stored
across periods. Chemically, Clorin is storable, but in practice the vast majority of households in
our sample appear to have exhausted the Clorin we sold them within the six weeks of our followup period. This suggests that it is reasonable to focus on within-period use. Implicitly, we are
1
Together, these assumptions mean that when we consider the effect of an increase in the offer price pit0 , we ignore
cross-channel substitution (households buying from our door-to-door marketers who would otherwise have bought
in a store) and intertemporal substitution (households buying from us who would otherwise have bought at a later
time). The demand parameters we estimate in our experiment are therefore unlikely to generalize (quantitatively) to
a permanent, market-wide change in the retail price R.
1
thereby assuming that if a household buys Clorin in some period and does not use it in drinking
water, it is exhausted in some other way. Field interviews we conducted after our study suggest
a plausible account is that households use Clorin to undertake household chores such as bleaching
sheets, washing vegetables, and cleaning toilets (see section EAdditional Survey Datasubsection.2.5
of the paper).2
In each period, each household makes two decisions. First, the household must decide whether
to buy Clorin. Then, if the household has purchased Clorin, it must decide whether to use Clorin
in its drinking water. We let bit ∈ {0, 1} be an indicator for whether household i buys Clorin
in period t. We let dit ∈ {0, 1} denote whether household i puts Clorin in its drinking water in
period t, with dit = 0 whenever bit = 0. We assume these decisions are made sequentially, so that
the decision to purchase is fixed when the household chooses whether to use Clorin in its drinking
water. Consistent with the discussion above, we can think of dit = 0 as performing household
chores (other than purifying drinking water), which, as seems reasonable, we assume is possible
with or without Clorin.
To apply Eyster’s (2002) framework, we need to specify both material payoffs and utility, the
latter incorporating the psychological desire to rationalize past choices. We begin by specifying the
material payoff function, which we normalize so that the payoff from not buying Clorin is 0.
Households differ in the benefits and costs of using Clorin in their drinking water. We will write
the net material payoff (in Kwacha) to household i from buying Clorin and using it in its drinking
water in period t as vi + εit − p̃it . Here, vi captures factors that are constant over time for a given
household and are known at the time of purchase, and εit captures time-varying shocks unknown
at the time of purchase.
Formally, we assume that vi is distributed i.i.d. across households, that εit is distributed i.i.d
across households and time periods, and that vi and εit are independent of one another and of
offer and transaction prices pit and p̃it (the last condition being maintained by experimental randomization). Consistent with the interpretation of εit as an unanticipated shock, we will normalize
E (εit ) = 0. To simplify exposition, we assume that both vi and εit are distributed according to
(possibly different) differentiable CDFs with full support on the real line, and that vi has finite
mean.
The terms vi and εit are general enough to accommodate a range of factors that affect a
household’s net return at the margin from using Clorin in its drinking water. For example, Clorin
is used when the household obtains water from its local source, and hence its use requires attention
from the female head of household at that time. In some households, the female head may have
many other chores to complete when obtaining water, making it hard to put Clorin in at the right
time (low vi ), whereas in others the female head may have few other responsibilities coincident
with obtaining water (high vi ). In addition, for a given household, variation in the household’s
day-to-day needs may lead to higher (low εit ) or lower (high εit ) demands on the female head’s
attention when she obtains water, affecting the incentive to use Clorin.3
The term vi can also capture variation across households in the return to purifying drinking
2
If our data are misleading, and in fact many households store and defer use of Clorin in drinking water, this force
would reduce the power of our experimental tests to detect sunk-cost effects. In the model below, sunk-cost effects
arise because households view it as a mistake to have purchased Clorin when they do not use it in their drinking
water. In a model with storability, sunk-cost effects of the sort we test for would instead require that households view
it as a mistake to have purchased Clorin when they do not use it in their drinking water in the period immediately
following purchase.
3
Many other interpretations are possible. For example, households may differ in their general level of concern
about water-borne illness, inducing variation in vi . After purchase, some households may hear about an especially
bad local incident of child diarrhea, leading to a high εit . Or they may hear that diarrhea episodes have been rare
recently, leading to a low εit .
2
water by means other than Clorin. For example, if boiling water were the main alternative to
Clorin, and if boiling water took more time to implement than using Clorin, then households whose
female head has a greater opportunity cost of time would have a higher vi , because at the margin
Clorin is displacing a less attractive option for such households.
To complete the specification of payoffs we must specify the payoff to buying Clorin and then
not using it in drinking water, using it instead for household cleaning. In that case, the benefit
of Clorin is the market value of the standard household cleaners whose use is offset by Clorin.
That interpretation suggests a small return from using Clorin for non-drinking-water purposes. For
example, data from a 2006 survey of retail prices show that the sodium hypochlorite in a bottle
of Clorin can be obtained from Jik, a more concentrated household bleach, for about 300 Kw.4
Moreover, our field experience suggests that households find products like Jik to be more effective
cleaners, suggesting that 300 Kw of Jik may deliver even more than one Clorin bottle’s worth
of cleaning power. Given the small benefit to Clorin not used in drinking water, we assume for
simplicity that the material payoff to buying Clorin and not using it in drinking water is −p̃it ,
implying that no household would buy Clorin if it were not possible to use it in drinking water.
Although that assumption is extreme and unlikely to hold exactly for all households, it seems likely
to be a reasonable approximation on average, based both on the calculations above and on our
conversations with female heads of household.5
To summarize, we can specify an (ex-post) material payoff function u (bit , dit ; p̃it , vi , εit ) that
relates choices to payoffs as a function of household characteristics and the transaction price:
u (0, 0; p̃it , vi , εit ) = 0
u (1, 0; p̃it , vi , εit ) = −p̃it
u (1, 1; p̃it , vi , εit ) = vi + εit − p̃it .
(Recall that dit = 0 whenever bit = 0, so u (0, 1; p̃it , vi , εit ) is undefined.)
A.2
Utility and Regret
To allow for psychological effects of prices, we will suppose that households have a taste for consistency, i.e. for taking actions in the present that rationalize their past choices. Following Eyster
(2002), we implement this assumption by positing that realized household utility U (bit , dit ; p̃it , vi , εit )
depends both on ex-post material payoff and on a regret function:
U (bit , dit ; p̃it , vi , εit ) ≡ u (bit , dit ; p̃it , vi , εit ) − ρr (bit , dit ; p̃it , vi , εit )
(1)
where r () denotes regret and ρ ≥ 0 indexes the importance of regret in the household’s utility
function.
We refer the reader to Eyster (2002) for a more careful exposition of the regret function. For4
As of the 2006 retailer survey, a 750ml container of Jik, consisting of 3.5% sodium hypochlorite, retailed for a
median of 7,000 Kw. A 250ml bottle of Clorin, consisting of 0.5% sodium hypochlorite, retailed for a median of 800
Kw. The amount of sodium hypochlorite in a container of Jik is therefore equivalent to the amount found in about
21 bottles of Clorin, so 333 Kw of Jik buys as much sodium hypochlorite as one bottle (800 Kw) of Clorin. Note
that this calculation ignores the convenience of Clorin’s smaller size (and hence lower price per sales unit). Recall,
however, that a week’s supply of cooking oil for a household costs about 4,800 Kw, suggesting that 7,000 Kw is not
a prohibitive outlay.
5
If the assumption were to fail, then the sunk-cost effects we derive below would operate only over the range of
transaction prices p̃it above the cost savings from using Clorin as a household cleaner.
3
mally, it is defined as follows
r (bit , dit ; p̃it , vi , εit ) ≡ u b̃ (dit ; p̃it , vi , εit ) , dit ; p̃it , vi , εit − u (bit , dit ; p̃it , vi , εit )
(2)
where
b̃ (dit ; p̃it , vi , εit ) ≡ arg max {u (b, dit ; p̃it , vi , εit )} .
b
Informally, given an action pair, regret is how much better the household’s material payoff would
be if it could re-choose its first stage action taking its second stage action, and the realization of
εit , as given.6 Households prefer to avoid regret, i.e. to choose actions that limit the harm done by
their past choices given their current ones.
The definition in (2) implies that
r (0, 0; p̃it , vi , εit ) = 0
(3)
r (1, 0; p̃it , vi , εit ) = p̃it
r (1, 1; p̃it , vi , εit ) = 0.
That is, regret is experienced only when the household buys Clorin but does not use it in its
drinking water, and is felt in proportion to the amount spent on Clorin.
In the model, then, if a household knew for sure that it would not use Clorin to purify its drinking
water, it would not buy Clorin. Households buy Clorin because they may use it in drinking water,
but if circumstances are such that Clorin is not used in drinking water, the household regrets its
purchase, and the regret experienced is greater the more the household paid for Clorin. Households
may therefore be willing to use Clorin in drinking water to avoid regret, i.e. to rationalize the past
decision to buy.
A.3
Choice and Identification
We can now specify how the household chooses whether to purchase Clorin and, if so, whether to
use it in drinking water. Beginning with the use decision, if the household has purchased Clorin,
the use decision is given by d∗it (p̃it , vi , εit ), where
d∗it (p̃it , vi , εit ) ≡ arg max U (1, d; p̃it , vi , εit ) .
d
This, in turn, implies that
d∗it (p̃it , vi , εit )
=
1
⇐⇒
≥
vi + εit
−ρp̃it .
That is, the household will use Clorin in its drinking water if the net benefit of doing so exceeds
the regret associated with not doing so. (Note that we have assumed for simplicity that ties are
broken in favor of use.)
When households are deciding whether to purchase Clorin in the first place, they do not an6
Note that, as we have defined it, regret depends on the realized transaction price p̃it , which is technically not
observed by non-purchasing households. However, because non-purchasing households do not make a use decision,
and because households are unaware of the possibility of a discount at the time of purchase, this is purely a notational
simplification, with no implications for behavior.
4
ticipate the discount, and do not know the realization of the time-varying shock εit . Therefore we
write the expected-utility-maximizing purchase decision as b∗it (pit , vi ), with
b∗it (pit , vi ) ≡ arg max EU (b, d∗it (pit , vi , εit ) ; pit , vi , εit )
b
where the expectation is taken over the distribution of the shocks εit . It follows that
b∗it (pit , vi )
=
1
⇐⇒
E [max (vi + εit , −ρpit ) | vi , pit ]
≥
pit
where we adopt the arbitrary rule that ties are broken in favor of purchasing.
Note that the household conditions its decision on the (known) household-specific benefit parameter vi and on the offer price pit . In particular, there exists a real-valued cutoff v ∗ (pit ), strictly
increasing in pit , such that the household purchases if and only if vi ≥ v ∗ (pit ). The proof of this
result is straightforward; economically, it follows from the fact that a higher vi increases the anticipated benefit from buying Clorin and a higher pi increases the anticipated cost (both financially
and psychologically).
Empirically, we do not observe the choice functions b∗it (pit , vi ) and d∗it (p̃it , vi , εit ), but rather
the empirical frequencies of different choices as a function of the prices pit and p̃it . To develop the
model’s empirical predictions, then, it will be helpful to write out these probabilities:
Pr (b∗it (pit , vi ) = 1 | pit , p̃it ) = Pr (vi ≥ v ∗ (pit ))
Pr (d∗it (p̃it , vi , εit ) = 1 | pit , p̃it ) = Pr (vi + εit ≥ −ρp̃it | vi ≥ v ∗ (pit ))
where the second probability conditions on the decision to purchase Clorin.
In a non-experimental period t 6= t0 , pit = p̃it = R, so there is no price variation and hence
no comparative statics to test. (The model does imply restrictions on the relationship between
prices in the experimental period and use in a non-experimental period, which we explore in online
appendix section B.)
In the experimental period t0 , by contrast, the above equations have two important empirical
implications about the relationship between prices and use.7
• The first, which we call the screening effect, is that, conditional on purchase, the probability
of use is higher the greater is pit0 . This is because a higher pit0 imposes a stricter (higher)
cutoff v ∗ (pit0 ) on anticipated benefits for buyers.
• The second, which we call the sunk-cost effect, is that, conditional on purchase, the probability
of use is increasing in the transaction price p̃it0 whenever ρ > 0. This is because a greater
transaction price implies a greater desire to rationalize the purchase decision (or, equivalently,
greater regret from not using Clorin in drinking water).
Observe that these two effects cannot be distinguished if transaction prices cannot vary independently of offer prices. If pit0 = p̃it0 for all i in some period t, then a finding that higher prices
causes more drinking water use conditional on purchase would be consistent with the presence of
7
A third, more obvious, implication is that the greater is the price of Clorin, the fewer households will purchase
it. Note that this result comes both from the traditional substitution effect, and from the fact that a higher price
implies greater anticipated regret in the case in which Clorin is not used in drinking water.
5
either the sunk-cost effect (ρ > 0) or the screening effect (heterogeneity in vi ), or both.8 Hence,
the two-stage pricing design solves an identification problem that would be present in data with
only a single price, even if that price were suitably exogenous.
It is worth noting that, although Eyster’s model is the most fully articulated single-agent theory
of sunk-cost effects of which we are aware, reasonable alternatives exist with possibly different
empirical implications. For example, if sunk-cost effects were driven by a desire to justify the ex
ante wisdom of one’s decision, rather than ex post wisdom of one’s decision as in Eyster’s framework,
it is possible that the offer price, rather than the transaction price, would influence use behavior.9
Such effects would confound our tests.10 On the other hand, Thaler’s (1980) prospect-theoretic
justification for sunk-cost effects hinges on a desire to avoid a feeling of loss experienced when one
does not realize consumption gains from a past purchase. In such a model transaction prices likely
would mediate the effect, suggesting that our tests may be valid under mechanisms other than the
one we model explicitly.
B
Intertemporal Implications of the Model
In the model, realized transaction prices p̃it0 in period t0 will not affect purchase or use behavior in
any period t 6= t0 : sunk-cost effects are localized to the period in which the transaction occurs. The
model does, however, have implications for the relationship between offer prices pit0 conditional on
purchase in period t0 and purchase and use behavior in periods t 6= t0 . In this appendix we briefly
summarize those implications. We also provide some empirical tests using data from our baseline
survey, reported in online appendix table 1. The baseline period can be thought of as a reasonable
approximation to period t0 − 1, in that any household owning Clorin as of the baseline survey would
have purchased it from a retailer (or health clinic). It is worth noting, however, that we did not
design our study to test these intertemporal implications, so the evidence reported below should
be thought of as preliminary.
Begin by considering the relationship between purchase behavior in the experiment and purchase
behavior in non-experimental periods. The model predicts that households purchasing in period
t0 are more likely to buy at other periods t 6= t0 , the greater is the offer price pit0 in period t0 . To
see this, observe that, for households that purchase in the experimental period t0 , we can write the
8
Note that the psychology of regret is also relevant for the magnitude of the screening effect, as the parameter ρ
partially determines the degree of price sensitivity in the purchase decision.
9
Sunk-cost effects could also operate through a desire to justify the purchase to another member of the household,
rather than to oneself (Prendergast and Stole, 1996). In that case, whether the offer or transaction price would influence use behavior through the sunk-cost mechanism would depend on the informational conditions in the household.
Because only the offer price is known to the buyer at the time of the purchase decision, a fully informed household
member would judge the intelligence of the decision based on the offer price. However, because only the transaction
price is actually implemented, it may be more observable to other members of the household than the offer price. In
that case, higher transaction prices would lead to greater use due to a desire to justify the purchase decision to other
household members, so our tests for sunk-cost effects would be valid.
10
Another possible confound arises if use depends not on the transaction price itself but on the discount, i.e. the
difference between the offer and transaction prices. We find no evidence in our data of a relationship between use
and the relative size of the discount—that is, the difference between offer and transaction prices, divided by the offer
price. If instead psychological effects operate through the absolute (as opposed to relative) size of the discount (offer
price minus transaction price), the resulting model is collinear with those we estimate, and is therefore not identified.
If the effect of a greater discount is to increase use, then our estimates will tend to overstate the screening effect
and to understate the sunk-cost effect. If greater discounts tend to decrease use, our estimates will understate the
screening effect and overstate the sunk-cost effect.
6
following for any non-experimental period t 6= t0 :
Pr (b∗it (R, vi ) = 1 | b∗it0 (pit0 , vi ) = 1, R, pit0 ) = Pr (vi ≥ v ∗ (R) | vi ≥ v ∗ (pit0 ))
with v ∗ (R) ≥ v ∗ (pit0 ). Because v ∗ () is increasing in pit0 , it follows directly that, conditional
on purchase in period t0 , the probability of purchase in a period t 6= t0 is greater the greater
is pit0 . Intuitively, the higher is a household’s demonstrated willingness to pay in period t0 , the
greater is its likelihood of purchasing at the retail price in other periods. We present a test of this
implication in column (1) of online appendix table 1. We measure purchase at baseline with an
indicator for whether our surveyor inventory indicates that the household had a non-empty Clorin
bottle at the time of the baseline survey. We find a marginally statistically significant positive
relationship between offer price and baseline purchase (conditional on purchase at the marketing
stage), consistent with the model.
Consider next the relationship between purchase behavior in the experiment and use behavior in
non-experimental periods. Perhaps somewhat surprisingly, the model predicts that, conditional on
purchase in the experiment and in a non-experimental period, the experimental offer price will be
unrelated to use in non-experimental periods. Formally, consider the expression for use conditional
on purchase in both the experimental period t0 and some non-experimental period t 6= t0 :
Pr (d∗it (R, vi , εit ) = 1 | b∗it0 (pit0 , vi ) = 1, R, pit0 ) = Pr (vi + εit ≥ −ρR | vi ≥ v ∗ (R) ∧ vi ≥ v ∗ (pit0 ))
That is, the set of households purchasing at both time t and time t0 are those for whom both
vi ≥ v ∗ (R) and vi ≥ v ∗ (pit0 ). However, because R ≥ pit0 , v ∗ (R) ≥ v ∗ (pit0 ), so that the two
conditions collapse to a single one:
Pr (d∗it (R, vi , εit ) = 1 | b∗it0 (pit0 , vi ) = 1, R, pit0 ) = Pr (vi + εit ≥ −ρR | vi ≥ v ∗ (R))
= Pr (d∗it (R, vi , εit ) = 1 | R)
Therefore we predict no relationship between offer price at time t0 and use behavior at time t 6= t0 .
Intuitively, this result comes about because anyone willing to pay R should also be willing to pay
pit0 ≤ R, so that offer prices in the experiment convey no new information about the composition
of households purchasing in non-experimental periods.11 Columns (2) and (3) of online appendix
table 1 present tests of this implication. Among those who had Clorin in their households as of the
baseline (our proxy for purchase at time t0 − 1) and who purchased Clorin in the marketing stage
(time t0 ), there is no relationship between offer price and self-reported or measured use at baseline,
consistent with the model. The coefficients are small, negative, and statistically insignificant.
Finally, consider the reverse question of how purchase behavior in non-experimental periods
affects our predictions for use in the experimental period. Following a logic parallel to the preceding
argument, it is straightforward to show that, conditional on purchase in a non-experimental period,
there should be no relationship between offer price in the experimental period and use in the
experimental period, holding constant the transaction price. That is, the screening effect should
be absent for households that purchase in non-experimental periods. In equations, this is because:
Pr (d∗it0 (p̃it0 , vi , εit ) = 1 | pit0 , p̃it0 , b∗it (R, vi ) = 1) = Pr (vi + εit ≥ −ρp̃it0 | vi ≥ v ∗ (R) ∧ vi ≥ v ∗ (pit0 ))
= Pr (vi + εit ≥ −ρp̃it0 | vi ≥ v ∗ (R)) .
11
Our model assumes a constant willingness-to-pay over time. A model with time-varying shocks to vi that are
known in advance of purchase to the household could yield a positive relationship between use in non-experimental
periods and experimental offer price. However, given that the non-experimental periods we study are close in time
to the experimental period, constant willingness-to-pay over time may be a reasonable approximation.
7
By contrast, households that did not purchase in non-experimental periods will still display the
screening effect, although with a different magnitude than the overall population:
Pr (d∗it0 (p̃it0 , vi , εit ) = 1 | pit0 , p̃it0 , b∗it (R, vi ) = 0) = Pr (vi + εit ≥ −ρp̃it0 | v ∗ (pit0 ) < vi ≤ v ∗ (R)) .
We test these implications in specifications reported in columns (4) through (7) of online appendix
table 1. Consistent with the model, among those who purchased at the marketing stage and had
Clorin at baseline, there is a statistically insignificant relationship between offer price and use at
follow-up. (We note, however, that due to small sample size our confidence intervals cannot rule
out nontrivial effects.) By contrast, among those who purchased at the marketing stage but did
not have Clorin in the home as of the baseline, there is a positive and statistically significant
relationship between offer price and use.
C
Implications of Survey Attrition
In this section we address the correlates of survey attrition and the implications of attrition for our
main findings.
Online appendix table 2 analyzes the determinants of attrition. Among those who bought
Clorin in the marketing stage, the rate of contact at follow-up is 89 percent. Column (1) of online
appendix table 2 shows that contact is somewhat related to observable household characteristics.
For example, households with an older female head, households with a married female head, and
households with more members are more likely to be reached at follow-up. An F -test of the joint
significance of our full vector of observables cannot quite reject the null that the observables have
no impact on the likelihood of contact (p = 0.102). Columns (2) and (3) of online appendix table 2
show that we cannot reject the null that the treatment variables (offer and transaction price) have
no effect on the likelihood of contact.
Lee (2009) shows that if treatment does not affect attrition, standard estimates of treatment
effects are valid, but are “local” to the population who are successfully contacted. Online appendix
table 2 shows that we cannot rule out statistically that there is no effect of treatment on attrition.
However, the power of these tests is finite, and it is therefore worthwhile asking whether effects
of treatment on attrition on the order of the point estimates in columns (2) and (3) of online
appendix table 2 are sufficient to affect the interpretation of our findings. To do this, we take the
point estimates in columns (2) and (3) of online appendix table 2, and assume that the households
removed (or added) from the follow-up sample by the treatment variable were either all users or
all non-users of Clorin. The resulting upper and lower bounds are extremely tight:
Specification
Use measure
Main tables
Lower bound
Upper bound
Screening effect
Self-reported Measured
0.0373
0.0321
0.0354
0.0302
0.0399
0.0346
Sunk-cost
Self-reported
0.0097
0.0092
0.0112
effect
Measured
-0.0071
-0.0075
-0.0055
Therefore, attrition due to treatment is unlikely to be a concern in our setting, and we can reliably
conduct inference local to the population of households reached in the follow-up survey.
A steeper challenge is to conduct inference on the entire population reached at marketing,
including those who are never observed. Below we produce upper and lower bounds for these
effects computed following Horowitz and Manski (2000). In particular, we compute residuals of the
treatment variables after partialling out all controls. For an upper bound we assign those attriters
8
with positive residuals to be users and those with negative residuals to be non-users. We reverse
the assignment to compute lower bounds. The bounds are wide:
Specification
Use measure
Main tables
Lower bound
Upper bound
Screening effect
Self-reported Measured
0.0373
0.0321
0.0013
-0.0037
0.0650
0.0605
Sunk-cost
Self-reported
0.0097
-0.0238
0.0423
effect
Measured
-0.0071
-0.0400
0.0263
These bounds admit slightly negative values for the screening effect and reasonably large positive
values for sunk-cost effects. It is therefore valuable to explore whether attrited households might
plausibly be close to the worst-case scenarios defined by the above bounds. By definition we cannot
directly analyze the use behavior of attrited households. However we can use observed variation
within the sample to attempt some inference about those we do not observe. We approach this in
two ways.
First, we estimate a logit analogue of column (1) of online appendix table 2. We then re-estimate
our main specifications, weighting by the inverse of the predicted probability from the logit model.
If all heterogeneity in treatment effects were related to observables, these estimates would be valid
for the entire population of households reached at the marketing stage. Weighted and unweighted
estimates are very similar:
Specification
Use measure
Main tables
Weighted
Screening effect
Self-reported Measured
0.0373
0.0321
0.0384
0.0311
Sunk-cost
Self-reported
0.0097
0.0068
effect
Measured
-0.0071
-0.0079
If anything, sunk-cost effects are weaker in the weighted specifications, and there is no systematic
direction of change for our estimates of screening effects.
Second, we examine heterogeneity in treatment effects related to how many attempts we had to
make in order to reach the household at follow-up. If attrited households are more similar to those
that were reached after the first attempt than to those we reached on the first attempt, comparing
these two groups may help to narrow the range of plausible scenarios within the bounds we provide
above. The results are below:
Specification
Use measure
Main tables
First attempt
Second or third attempt
Screening effect
Self-reported Measured
0.0373
0.0321
0.0343
0.0284
0.0402
0.0366
Sunk-cost
Self-reported
0.0097
-0.0032
0.0406
effect
Measured
-0.0071
-0.0116
0.0129
The differences between the two groups are never statistically significant. If anything we find
that screening effects are larger among the households that required a second or third attempt
before contact, indicating that difficulty of contact is not associated with weaker screening effects.
Directionally, difficulty of contact is associated with stronger sunk-cost effects, though the difference
is economically much larger for self-reported than for measured use.
We take three lessons from the analysis in this section. First, there is no evidence of an effect
of treatment on attrition, and even at the point estimates for those effects there is little reason to
be concerned about the validity of our main estimates for the population of households reached
9
in the follow-up. Second, worst-case bounds for our main specifications are wide, indicating that
we cannot rule out reversals of our conclusions among the overall population if attrited households
differ radically from those we observe. Third, an analysis of heterogeneity of treatment effects
with respect to both observable characteristics and the difficulty of re-contact do not indicate such
radical differences with respect to screening effects. If anything the analysis suggests we might
expect somewhat stronger screening effects on the overall population. However, point estimates
do indicate that sunk-cost effects may be larger for households that were more difficult to reach,
indicating that some caution is warranted in interpreting the power of our sunk-cost tests.
D
Additional Implications of Sunk-cost Psychology
In this section we empirically test empirical implications of extensions to the sunk-cost model that
we formalize in section A.
In the model, we assume that the regret parameter ρ is identical across households. If there
is heterogeneity in this parameter, then, all else equal, households with higher values of ρ should
exhibit a lower propensity to purchase Clorin, because these households anticipate the possibility of
regret if they purchase and do not use Clorin in drinking water. We proxy for the regret parameter
ρ using households’ sunk-cost status defined by their responses to hypothetical choices. We assume
that sunk-cost status is orthogonal to other drivers of purchase behavior, conditional on our set
of baseline controls. We can then test for an effect of ρ on purchase propensity by regressing a
dummy for whether the household purchased Clorin on a dummy for sunk-cost status and our set of
baseline controls. Column (1A) of online appendix table 3 shows that we find, consistent with this
prediction, that sunk-cost households have a lower propensity to purchase Clorin than non-sunkcost households, although the coefficient is statistically insignificant. As a further caveat, we note
also that sunk-cost status is correlated with the baseline controls in the model. In a regression of
sunk-cost status on baseline controls, an F-test of the null hypothesis that baseline controls jointly
do not affect sunk-cost status, we can reject the null at conventional significance levels (p = 0.0062).
This suggests a note of caution in interpreting the coefficient in column (1A), as sunk-cost status
may be correlated with unobservable determinants of purchase propensity.
A related hypothesis is that sunk-cost households are more price-sensitive than non-sunk-cost
households, as higher prices increase the risk of utility losses due to regret. Columns (2A) and
(3A) show that price-sensitivity is fairly similar between sunk-cost and non-sunk-cost groups. The
difference in the effect of a 100 Kw increase in price on the propensity to purchase Clorin is
economically similar and statistically indistinguishable between the two groups.
In the model, feelings of regret arise in equilibrium because households are subject to expost shocks to the net value of using Clorin in drinking water. Although some shocks (hassle,
forgetting, disease episodes, etc.) could in principle affect any household, other shocks, such as
learning about the taste or other properties of Clorin itself, are more likely to affect households
with less prior information about Clorin. Because our sample largely consists of households with
past experience with Clorin, our main specifications might therefore miss important sunk-cost
effects for those without such experience. In panel B of online appendix table 3 we ask whether
the magnitude of sunk-cost effects is related to whether a household has ever used Clorin in the
past. If anything, we find that sunk-cost effects are statistically significantly lower for households
without prior experience with Clorin. Such households are at least marginally significantly less
likely to use Clorin the higher is the transaction price, with confidence intervals that can rule out
sizable positive effects of transaction price on use. Among those who have used Clorin in the past,
we continue to find small and statistically insignificant effects of transaction price on use. Because
10
these hypothesis tests were not part of our original design, future work will be needed to determine
whether the surprising negative effects we find for never-users are robust and, if so, what mechanism
underlies them. At the very least, these specifications suggest that our main specifications do not
conceal important positive effects of transaction prices on use for inexperienced households.
11
12
614
No. of obs.
133
-0.0067
(0.0245)
Yes
(2)
Water currently treated
with Clorin?
(baseline; self-reported)
133
-0.0093
(0.0265)
Yes
(3)
Drinking water contains
free chlorine?
(baseline; measured)
117
-0.0289
(0.0288)
Yes
429
0.0512
(0.0169)
No
(4)
(5)
Water currently treated
with Clorin?
(follow-up; self-reported)
117
-0.0046
(0.0294)
Yes
425
0.0386
(0.0171)
No
(6)
(7)
Drinking water contains
free chlorine?
(follow-up; measured)
Notes: Standard errors in parentheses. See online appendix section B for details. Sample consists of households who purchased Clorin at marketing
stage.
0.0182
(0.0104)
All
(1)
Have Clorin
in household?
(baseline; inventory)
Offer price
(100 Kw)
Sample: Clorin in
home at baseline?
Dependent variable
Online Appendix Table 1 Intertemporal implications of the model
Online Appendix Table 2 Determinants of sample attrition
(1)
Offer price (100 Kw)
(2)
(3)
-0.0042
(0.0090)
Transaction price (100 Kw)
0.0063
(0.0080)
Water currently treated with Clorin?
-0.0097
-0.0165
-0.0092
(baseline; self-reported)
(0.0336)
(0.0339)
(0.0338)
Drinking water contains free chlorine?
-0.0034
-0.0030
-0.0057
(baseline; measured)
(0.0271)
(0.0274)
(0.0274)
0.0028
0.0044
0.0004
(index)
(0.0481)
(0.0484)
(0.0487)
Use of soap after using toilet
-0.0194
-0.0249
-0.0231
(index)
(0.0491)
(0.0492)
(0.0496)
0.0882
0.0878
0.0838
(0.0686)
(0.0689)
(0.0690)
Use of soap before handling food
Attitude toward water purification
(index)
Age in years
Ever attended school?
Years of completed schooling
Currently married?
Currently pregnant?
Ever given birth to any children?
No. of children in household under age 5
No. of people in household
Share of durables owned
0.0031
0.0033
0.0034
(0.0015)
(0.0015)
(0.0015)
-0.0057
-0.0129
-0.0035
(0.0552)
(0.0554)
(0.0556)
0.0077
0.0083
0.0078
(0.0059)
(0.0059)
(0.0059)
0.0775
0.0751
0.0811
(0.0362)
(0.0364)
(0.0364)
-0.0400
-0.0439
-0.0410
(0.0428)
(0.0429)
(0.0430)
-0.0146
-0.0108
-0.0242
(0.0560)
(0.0562)
(0.0563)
-0.0099
-0.0120
-0.0105
(0.0177)
(0.0177)
(0.0178)
0.0119
0.0126
0.0121
(0.0057)
(0.0057)
(0.0058)
0.0040
-0.0037
0.0020
(0.0866)
(0.0867)
(0.0870)
Locality fixed effects?
YES
YES
YES
Fixed effects for offer price?
NO
NO
YES
Fixed effects for transaction price?
NO
YES
NO
F -test that control coefficients are 0
p-value of F -test
1.45
1.54
1.50
0.1015
0.0712
0.0837
605
605
605
Number of observations
Notes: Standard errors in parentheses. All variables measured as of baseline survey. Offer price and transaction price variables excluded from F -tests. Sample includes all households who purchased Clorin at marketing
stage and for whom all observables are nonmissing.
13
Online Appendix Table 3 Additional implications of sunk-cost psychology
Panel A: Take-up by sunk-cost status
(1A)
(2A)
(3A)
Dependent variable
Purchased Clorin?
Sample
All
Sunk-cost household?
-0.0606
(0.0396)
Offer price
(100 Kw)
-0.0661
(0.0214)
Difference
(sunk-cost vs. non-sunk-cost)
Baseline controls?
Sample mean of dep. var.
No. of obs.
Sunk-cost household?
Yes
No
—
0.0012
(0.0242)
YES
YES
YES
0.6130
876
0.5567
203
0.6300
673
Panel B: Sunk-cost effects by ever-use status
(1B)
(2B)
Dependent variable
Water currently treated
with Clorin?
(follow-up; self-reported)
Sample
Transaction price
(100 Kw)
-0.0673
(0.0113)
Ever used Clorin?
Yes
No
0.0204
(0.0147)
Difference
(ever used vs. never used)
-0.0648
(0.0382)
(3B)
(4B)
Drinking water contains
free chlorine?
(follow-up; measured)
Ever used Clorin?
Yes
No
0.0018
(0.0146)
0.0853
(0.0410)
-0.0889
(0.0378)
0.0907
(0.0405)
Offer price fixed effects?
YES
YES
YES
YES
Baseline controls?
YES
YES
YES
YES
0.5308
439
0.4388
98
0.5459
436
0.4948
97
Sample mean of dep. var.
No. of obs.
Notes: Standard errors in parentheses. See online appendix section D for details.
14
References
[1] Erik Eyster. Rationalizing the past: A taste for consistency. Nuffield College Mimeograph,
November 2002.
[2] Joel L. Horowitz and Charles F. Manski. Nonparametric analysis of randomized experiments
with missing covariate and outcome data. Journal of the American Statistical Association,
95(449):77–84, 2000.
[3] David S. Lee. Training, wages, and sample selection: Estimating sharp bounds on treatment
effects. Review of Economic Studies, 76(3):1071–1102, 2009.
[4] Canice Prendergast and Lars Stole. Impetuous youngsters and jaded old-timers: Acquiring a
reputation for learning. Journal of Political Economy, 104(6):1105–1134, December 1996.
[5] Richard Thaler. Toward a positive theory of consumer choice. Journal of Economic Behavior
and Organization, 1(1):39–60, March 1980.
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